from __future__ import annotations


def 				lowerCAmelCase__       (			a__ )      ->list:




  '''simple docstring'''

  if len(a__ ) == 0:
    return []
  _UpperCamelCase      ,						_UpperCamelCase           =    min(a__ ), max(a__ )
  _UpperCamelCase           =    int(max_value - min_value ) + 1
  _UpperCamelCase           =    [[] for _ in range(a__ )]

  for i in my_list:
    buckets[int(i - min_value )].append(a__ )

  return [v for bucket in buckets for v in sorted(a__ )]


if __name__ == "__main__":
   from doctest import testmod

   testmod()
   assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
   assert bucket_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]





from math import isqrt, loga


def 				lowerCAmelCase__       (			a__ )      ->list[int]:




  '''simple docstring'''

  _UpperCamelCase           =    [True] * max_number
  for i in range(2    ,     isqrt(max_number - 1 ) + 1 ):
    if is_prime[i]:
      for j in range(i**2    ,     a__    ,     a__ ):
        _UpperCamelCase           =    False

  return [i for i in range(2    ,     a__ ) if is_prime[i]]


def 				lowerCAmelCase__       (			a__ = 800_800    ,     a__ = 800_800 )      ->int:




  '''simple docstring'''

  _UpperCamelCase           =    degree * loga(a__ )
  _UpperCamelCase           =    int(a__ )
  _UpperCamelCase           =    calculate_prime_numbers(a__ )

  _UpperCamelCase           =    0
  _UpperCamelCase           =    0
  _UpperCamelCase           =    len(a__ ) - 1
  while left < right:
    while (
        prime_numbers[right] * loga(prime_numbers[left] )
        + prime_numbers[left] * loga(prime_numbers[right] )
        > upper_bound
    ):
      right -= 1
    hybrid_integers_count += right - left
    left += 1

  return hybrid_integers_count


if __name__ == "__main__":
   print(F"{solution() = }")




